Given that $\displaystyle x = e^t$, find $\displaystyle \frac{dy}{dx}$ in terms of $\displaystyle \frac{dy}{dt}$ and show that

$\displaystyle \frac{d^2y}{dx^2} = e^{-2}\left(\frac{d^2y}{dt^2} -\frac{dy}{dt}\right)$.

EDIT:Sorry, It is a typo, it should be $\displaystyle \frac{d^2y}{dx^2} = e^{-2t}\left(\frac{d^2y}{dt^2} -\frac{dy}{dt}\right)$.